WASHINGTON — Nothing touches off a political war in the Senate like proposals to tinker with the arcane rules that govern the often creaky chamber. Talk of eliminating the filibuster is called the nuclear option for a reason.

But Senator Lamar Alexander of Tennessee, the cerebral former Republican governor and cabinet member, may have come up with a novel approach to winning support for the changes that many, if not most, of his colleagues agree are overdue — and to enact them without starting the congressional equivalent of Armageddon.

His idea? Use the next few months to develop, debate and approve proposals to make the Senate more efficient, but then agree not to institute the changes until 2017 — after next year’s election. With no certainty about which party will win the majority next November, the thinking goes, both Republicans and Democrats might be enticed to roll the dice and embrace changes since there would not be an obvious advantage to advance for either party.

“We think we are more likely to get a consensus that way,” said Mr. Alexander, who is working with five fellow Republicans to explore what can be done to improve how the Senate does — or does not — function.

His goal is to institute changes with the support of at least 67 senators, the traditional threshold, as opposed to the simple majority Democrats employed two years ago to weaken filibusters against Obama administration nominees.

Democrats, currently in the minority, are open to the concept.

“Now that each side has served in the minority and majority, we can come at it from both perspectives,” said Senator Chuck Schumer of New York, expected to be the Democratic leader in 2017. “We could come up with something good.”

The move would represent a risk for both parties, one they might later regret should their power be diluted if they come out on the wrong end of the election. But there is a growing sense that something serious needs to be done to make the Senate more functional, or its public image will continue to decline.

“It is hard to get here, and it is hard to stay here,” Mr. Alexander said of the Senate. “And while you are here, you might as well amount to something. Most senators would like to have a more productive Senate.”

The intensifying discussion of revamping Senate rules comes as House Republicans are clamoring for their Senate comrades to use their majority status to unilaterally bust the filibuster so they can send more politically charged bills like a repeal of the Affordable Care Act to President Obama’s desk. But to many Senate Republicans, it makes no sense to take such a provocative step to simply send a bill to the White House, only to see it vetoed.

Mr. Alexander said he used to believe that a “change in behavior” was all that was needed to make the Senate more productive. But he has come around to the idea that structural changes are necessary given the rise in partisanship that has tied the Senate in knots.

“The changes we are likely to settle on probably won’t be complicated. The Senate is complicated enough,” he said. “I still think you want a United States Senate that stops and thinks when the passions of the country are overwhelming the House of Representatives. But there could be a Senate that is more efficient. There is too much dead time on the Senate floor.”

Part of the Senate’s problem revolves around the “motion to proceed,” a once routine vote to put a bill or nomination on the floor that has become a favorite target of those wanting to slam on the brakes. Senator Mitch McConnell of Kentucky, the current majority leader, was a pioneer of filibustering the motion to proceed, and Democrats this year embraced that approach to hold up appropriations bills and other legislation.

Under various proposals, the ability to filibuster the preliminary motion, particularly on appropriations bills, would be eliminated, allowing a measure to at least come up for debate. Backers of the idea believe that once a bill hits the floor and lawmakers get a chance to shape it, they will be less inclined to block a final vote. However, it would still be subject to a filibuster on final passage, meaning 41 senators could kill it.

Another potential area of change is the requirement that extensive amounts of time must lapse before the Senate can act, such as the mandatory “intervening day” between filing a motion to cut off debate and holding the vote on it. The idea of guaranteeing a minimum number of amendments for each side on bills is also being considered.

Mr. Alexander and his Republican colleagues — Senators Roy Blunt of Missouri, chairman of the Rules Committee, and Cory Gardner of Colorado, James Lankford of Oklahoma, Ben Sasse of Nebraska and Thom Tillis of North Carolina, all freshmen — have been meeting with legislative experts on Senate procedures, including Dave Shiappa and Martin B. Gold, former floor officials.

They intend to present their recommendations to Senate Republicans soon and then reach out to Democrats who have expressed interest in changes to rules, including Senators Jeff Merkley of Oregon, Tom Udall of New Mexico and Mr. Schumer.

The continuing talks might not mollify Republicans frustrated by the Senate’s frequent state of suspended animation. But Mr. Alexander cautioned those who want to kill the filibuster now that Republicans control the House and Senate. Since World War II, he noted, Republicans have controlled the House, Senate and White House for just six years compared with 22 for Democrats, who not long ago had a 60-vote, filibuster-proof Senate majority.

“Conservatives need to remember that having complete Democratic control without a filibuster is how we got Obamacare and how we could lose the right-to-work laws in the two dozen states that now have them,” he said. “If a freight train ran through the House, it would just keep running through the Senate.”